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Quantum Physics

Title:
Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators

Abstract: Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator
can be uniquely written of a particular form, which we call the Matsumoto-Amano
normal form. In this mostly expository paper, we give a detailed and
streamlined presentation of Matsumoto and Amano's results, simplifying some
proofs along the way. We also point out some corollaries to Matsumoto and
Amano's work, including an intrinsic characterization of the Clifford+T
subgroup of SO(3), which also yields an efficient T-optimal exact single-qubit
synthesis algorithm. Interestingly, this also gives an alternative proof of
Kliuchnikov, Maslov, and Mosca's exact synthesis result for the Clifford+T
subgroup of U(2).